Question

The graph of a function is shown below.

Describe the behavior of this function in terms of its intercepts, roots, maxima, minima and end behaviors. Classify the function as linear, quadratic, or another polynomial.

Answer 1

Quadratic function with intercepts at 1 and 3, so with a function of (x-1)(x-3), or x^2-4x+3. Y-intercept at (0,3). Positive end behavior. Minimum at (2,-1), with an infinite positive range

Answer 2

Explanation:

In the graph, the graph crosses x axis at 1 and 3

So zeros are 1 and 3

Also x intercepts are (1,0) and (3,0)

The graph where it crosses y axis is the y intercept

the graph crosses y intercept at y=3

so y intercept is (0,3)

The graph reaches minimum at (2,-1)

End behavior

When x approaches ∞, y goes to ∞

When x approaches -∞, y goes to ∞

so y is positive for all values of x

The graph is a graph of parabola . It is a U shaped

The graph of quadratic polynomial is always U shaped Parabola

So graph is quadratic